On the structure of isometrically embeddable metric spaces

Kathleen Nowak, Carlos Ortiz Marrero, Stephen Young
2022 The Electronic Journal of Linear Algebra  
Since its popularization in the 1970s, the Fiedler vector of a graph has become a standard tool for clustering of the vertices of the graph. Recently, Mendel and Noar, Dumitriu and Radcliffe, and Radcliffe and Williamson have introduced geometric generalizations of the Fiedler vector. Motivated by questions stemming from their work, we provide structural characterizations for when a finite metric space can be isometrically embedded in a Hilbert space.
doi:10.13001/ela.2022.6891 fatcat:6up5doqvpfdsxbdjwl56m5lpmi